Nucleation in a slit pore

Classical nucleation of vapor between hydrophobic plates

In this work, an extended classical nucleation theory (CNT), including line tension, is used to disentangle classical and non-classical effects in the nucleation of vapor from a liquid confined between two hydrophobic plates at a nanometer distance. The proposed approach allowed us to gauge, from the available simulation work, the importance of elusive nanoscale effects, such as line tension and non-classical modifications of the nucleation mechanism. Surprisingly, the purely macroscopic theory is found to be in quantitative accord with the microscopic data, even for plate distances as small as 2 nm, whereas in extreme confinement ([Formula: see text] nm), the CNT approximations proved to be unsatisfactory. These results suggest how classical nucleation theory still offers a computationally inexpensive and predictive tool useful in all domains where nanoconfined evaporation occurs—including nanotechnology, surface science, and biology.

Machine-Learned Free Energy Surfaces for Capillary Condensation and Evaporation in Mesopores

Using molecular simulations, we study the processes of capillary condensation and capillary evaporation in model mesopores. To determine the phase transition pathway, as well as the corresponding free energy profile, we carry out enhanced sampling molecular simulations using entropy as a reaction coordinate to map the onset of order during the condensation process and of disorder during the evaporation process. The structural analysis shows the role played by intermediate states, characterized by the onset of capillary liquid bridges and bubbles. We also analyze the dependence of the free energy barrier on the pore width. Furthermore, we propose a method to build a machine learning model for the prediction of the free energy surfaces underlying capillary phase transition processes in mesopores.

Nucleation of Capillary Bridges and Bubbles in Nanoconfined CO2

Using molecular simulation, we examine the capillary condensation and the capillary evaporation of CO₂ in cylindrical nanopores. More specifically, we employ the recently developed μV T-S method to determine the microscopic mechanism associated with these processes and the corresponding free energy profiles. We calculate the free energy barrier for capillary condensation and identify that the key step consists in the nucleation of a liquid bridge of a critical size. Similarly, the free energy maximum found for the capillary evaporation process is found to correspond to the nucleation of a vapor bubble of a critical size. In addition, we assess the impact of the strength of the wall-fluid on the height of the free energy barrier and on the critical size of liquid bridges (condensation process) and vapor bubbles (evaporation process). We observe that the height of the free energy barrier increases with the strength of the wall-fluid interactions. Finally, we build a theoretical model, based on capillary theory, to rationalize our findings. In particular, the simulation results reveal a linear scaling of the free energy barrier with the critical size, in excellent agreement with the theoretical predictions.

Prediction of Contact Angles and Density Profiles of Sessile Droplets Using Classical Density Functional Theory Based on the PCP-SAFT Equation of State

This study demonstrates the capability of the density functional theory (DFT) formalism to predict contact angles and density profiles of model fluids and of real substances in good quantitative agreement with molecular simulations and experimental data. The DFT problem is written in cylindrical coordinates, and the solid-fluid interactions are defined as external potentials toward the fluid phase. Monte Carlo (MC) molecular simulations are conducted in order to assess the density profiles resulting from the Helmholtz energy functional used in the DFT formalism. Good quantitative agreement between DFT predictions and MC results for Lennard-Jones and ethane nanodroplets is observed, both for density profiles and for contact angles. That comparison suggests, first, that the Helmholtz energy functional proposed in a previous study [ Sauer , E. ; Gross , J. Ind. Eng. Chem. Res. 56 , 2017 , 4119 - 4135 ] is suitable for three-phase contact lines and, second, that Lagrange multipliers can be used to constrain the number of molecules, similar to a canonical ensemble. Experiments of sessile droplets on solid surfaces are performed to assess whether a real solid with its microscopic roughness can be described through a simple model potential. Comparison of DFT results to experimental data is done for a Teflon surface because Teflon can be regarded as a substrate exhibiting only attractive interactions of van der Waals type. It is shown that the real solid can be described as a perfectly planar solid with effective solvent-to-solid interactions, defined through a single adjustable parameter for the solid. Subsequent predictions for the contact angle of eight solvents, including polar components such as water, are found in very good agreement to experimental data using simple Berthelot-Lorentz combining rules. For the eight investigated solvents, we find mean absolute deviations of 3.77°.

Heterogeneous nucleation of a droplet pinned at a chemically inhomogeneous substrate: A simulation study of the two-dimensional Ising case

Heterogeneous nucleation is studied by Monte Carlo simulations and phenomenological theory, using the two-dimensional lattice gas model with suitable boundary fields. A chemical inhomogeneity of length b at one boundary favors the liquid phase, while elsewhere the vapor is favored. Switching on the bulk field H_b favoring the liquid, nucleation and growth of the liquid phase starting from the region of the chemical inhomogeneity are analyzed. Three regimes occur: for small fields, H_b<H_b^crit, the critical droplet radius is so large that a critical droplet having the contact angle θ_c required by Young's equation in the region of the chemical inhomogeneity does not yet "fit" there since the baseline length of the circle-cut sphere droplet would exceed b. For H_b^crit<H_b<H_b^*, such droplets fit inside the inhomogeneity and are indeed found in simulations with large enough observation times, but these droplets remain pinned to the chemical inhomogeneity when their baseline has grown to the length b. Assuming that these pinned droplets have a circle cut shape and effective contact angles θ_eff in the regime θ_c < θ_eff < π/2, the density excess due to these droplets can be predicted and is found to be in reasonable agreement with the simulation results. On general grounds, one can predict that the effective contact angle θ_eff and the excess density of the droplets, scaled by b, are functions of the product bH_b but do not depend on both variables separately. Since the free energy barrier for the "depinning" of the droplet (i.e., growth of θ_eff to π - θ_c) vanishes when θ_eff approaches π/2, in practice only angles θ_eff up to about θ_eff^max≃70° were observed. For larger fields (H_b>H_b^*), the droplets nucleated at the chemical inhomogeneity grow to the full system size. While the relaxation time for the growth scales as τ_G∝H_b^-1, the nucleation time τ_N scales as lnτ_N∝H_b^-1. However, the prefactor in the latter relation, as evaluated for our simulations results, is not in accord with an extension of the Volmer-Turnbull theory to two-dimensions, when the theoretical contact angle θ_c is used.

Free-energy barriers for crystal nucleation from fluid phases

Monte Carlo simulations of crystal nuclei coexisting with the fluid phase in thermal equilibrium in finite volumes are presented and analyzed, for fluid densities from dense melts to the vapor. Generalizing the lever rule for two-phase coexistence in the canonical ensemble to finite volume, "measurements" of the nucleus volume together with the pressure and chemical potential of the surrounding fluid allows us to extract the surface free energy of the nucleus. Neither the knowledge of the (in general nonspherical) nucleus shape nor of the angle-dependent interface tension is required for this task. The feasibility of the approach is demonstrated for a variant of the Asakura-Oosawa model for colloid-polymer mixtures, which form face-centered cubic colloidal crystals. For a polymer to colloid size ratio of 0.15, the colloid packing fraction in the fluid phase can be varied from melt values to zero by the variation of an effective attractive potential between the colloids. It is found that the approximation of spherical crystal nuclei often underestimates actual nucleation barriers significantly. Nucleation barriers are found to scale as ΔF^{*}=(4π/3)^{1/3}γ[over ¯](V^{*})^{2/3}+const with the nucleus volume V^{*}, and the effective surface tension γ[over ¯] that accounts implicitly for the nonspherical shape can be precisely estimated.

Superheating and homogeneous single bubble nucleation in a solid-state nanopore

We demonstrate extreme superheating and single bubble nucleation in an electrolyte solution within a nanopore in a thin silicon nitride membrane. The high temperatures are achieved by Joule heating from a highly focused ionic current induced to flow through the pore by modest voltage biases. Conductance, nucleation, and bubble evolution are monitored electronically and optically. Temperatures near the thermodynamic limit of superheat are achieved just before bubble nucleation with the system at atmospheric pressure. Bubble nucleation is homogeneous and highly reproducible. This nanopore approach more generally suggests broad application to the excitation, detection, and characterization of highly metastable states of matter.

Curvature of capillary bridges as a competition between wetting and confinement

We consider the shape evolution of non-axisymmetric capillary bridges in slit pore geometry as the pore height is increased at constant volume. Experiments and finite element simulations using Surface Evolver have shown that as the height of the pore is increased the mean curvature of the bridge, and hence Laplace pressure, changes its sign from negative to positive. Here we propose an intuitive explanation of this surprising phenomenon. We suggest that it is the balance between the confinement and the wetting properties of the supporting strips that causes the change in sign of the Laplace pressure. The theory proposed relies on three simple approximations, which are tested individually, and is in good agreement with experiments and simulations in the regime where the curvature transition from negative to positive takes place. Theoretical arguments take into account only the wetting properties and geometry of the system (the width and height of the pore). Along with the formula for the curvature, we derive also a relation for the pinning angle of the capillary bridge, which is also verified experimentally.

Size dependence of the contact angle of a nanodrop in a nanocavity: density functional theory considerations

The dependence of the contact angles of nanodrops of Lennard-Jones type fluids in nanocavities on their sizes are calculated using a nonlocal density functional theory in a canonical ensemble. Cavities of various radii and depths, various temperatures, as well as various values of the energy parameter of the fluid-solid interactions were considered. It is argued that this dependence might affect strongly, for instance, the rate of heterogeneous nucleation on rough surfaces, which is usually calculated under the assumption of constant contact angle.

Microscopic description of a drop on a solid surface

Two approaches recently suggested for the treatment of macro- or nanodrops on smooth or rough, planar or curved, solid surfaces, based on fluid-fluid and fluid-solid interaction potentials are reviewed. The first one employs the minimization of the total potential energy of a drop by assuming that the drop has a well defined profile and a constant liquid density in its entire volume with the exception of the monolayer nearest to the surface where the density has a different value. As a result, a differential equation for the drop profile as well as the necessary boundary conditions are derived which involve the parameters of the interaction potentials and do not contain such macroscopic characteristics as the surface tensions. As a consequence, the macroscopic and microscopic contact angles which the drop profile makes with the surface can be calculated. The macroscopic angle is obtained via the extrapolation of the circular part of the drop profile valid at some distance from the surface up to the solid surface. The microscopic angle is formed at the intersection of the real profile (which is not circular near the surface) with the surface. The theory provides a relation between these two angles. The ranges of the microscopic parameters of the interaction potentials for which (i) the drop can have any height (volume), (ii) the drop can have a restricted height but unrestricted volume, and (iii) a drop cannot be formed on the surface were identified. The theory was also extended to the description of a drop on a rough surface. The second approach is based on a nonlocal density functional theory (DFT), which accounts for the inhomogeneity of the liquid density and temperature effects, features which are missing in the first approach. Although the computational difficulties restrict its application to drops of only several nanometers, the theory can be applied indirectly to macrodrops by calculating the surface tensions and using the Young equation to determine the contact angle. Employing the canonical ensemble version of the DFT, nanodrops on smooth and rough solid surfaces could be investigated and their characteristics, such as the drop profile, contact angle, as well as the fluid density distribution inside the drop can be determined as functions of the parameters of the interaction potentials and temperature. It was found that the contact angle of the drop has a simple (quasi)universal dependence on the energy parameter epsilon(fs) of the fluid-solid interaction potential and temperature. The main feature of this dependence is the existence of a fixed value theta(0) of the contact angle theta which separates the solid substrates (characterized by the energy parameter epsilon(fs) of the fluid-solid interaction potential) into two classes with respect to their temperature dependence. For theta>theta(0) the contact angle monotonously increases and for theta<theta(0) monotonously decreases with increasing temperature. For theta=theta(0) the contact angle is independent of temperature. The results obtained via DFT were also applied to check the validity of the macroscopic phenomenological equations (Cassie-Baxter and Wenzel equations) for drops on rough surfaces, and of the equation for the sticking force of a drop on an inclined surface.

Symmetry breaking in confined fluids

The recent progress in the theoretical investigation of the symmetry breaking (the existence of a stable state of a system, in which the symmetry is lower than the symmetry of the system itself) for classical and quantum fluids is reviewed. The emphasis is on the conditions which cause symmetry breaking in the density distribution for one component fluids and binary mixtures confined in a closed nanoslit between identical solid walls. The existing studies have revealed that two kinds of symmetry breaking can occur in such systems. First, a one-dimensional symmetry breaking occurs only in the direction normal to the walls as a fluid density profile asymmetric with respect of the middle of the slit and uniform in any direction parallel to the walls. Second, a two-dimensional symmetry breaking occurs in the fluid density distribution which is nonuniform in one of the directions parallel to the walls and asymmetrical in the direction normal to the walls. It manifests through liquid bumps and bridges in the fluid density distribution. For one component fluids, conditions of existence of symmetry breaking are provided in terms of the average fluid density, strength of fluid-solid interactions, distance at which the solid wall generates a hard core repulsion, and temperature. In the case of binary mixtures, the occurrence of symmetry breaking also depends on the composition of the confined mixtures.

Heterogeneous nucleation at a wall near a wetting transition: a Monte Carlo test of the classical theory

While for a slightly supersaturated vapor the free energy barrier ΔF(hom)(*), which needs to be overcome in a homogeneous nucleation event, may be extremely large, nucleation is typically much easier at the walls of the container in which the vapor is located. While no nucleation barrier exists if the walls are wet, for incomplete wetting of the walls, described via a nonzero contact angle Θ, classical theory predicts that nucleation happens through sphere-cap-shaped droplets attracted to the wall, and their formation energy is ΔF(het)(*) = ΔF(hom)(*)f(Θ), with f(Θ) = (1-cosΘ)(2)(2+cosΘ)/4. This prediction is tested through simulations for the simple cubic lattice gas model with nearest-neighbor interactions. The attractive wall is described in terms of a local 'surface field', leading to a critical wetting transition. The variation of the contact angle with the strength of the surface field is determined by using thermodynamic integration methods to obtain the wall free energies which enter Young's equation. Obtaining the chemical potential as a function of the density for a system with periodic boundary conditions (and no walls), the droplet free energy of a spherical droplet in the bulk is obtained for a wide range of droplet radii. Similarly, ΔF(het)(*) is obtained for a system with two parallel walls. We find that the classical theory is fairly accurate if a line tension correction for the contact angle is taken into account.

Nucleation and hysteresis of vapor-liquid phase transitions in confined spaces: effects of fluid-wall interaction

In this work, we propose a method to stabilize a nucleus in the framework of lattice density-functional theory (LDFT) by imposing a suitable constraint. Using this method, the shape of critical nucleus and height of the nucleation barrier can be determined without using a predefined nucleus as input. As an application of this method, we study the nucleation behavior of vapor-liquid transition in nanosquare pores with infinite length and relate the observed hysteresis loop on an adsorption isotherm to the nucleation mechanism. According to the dependence of hysteresis and the nucleation mechanism on the fluid-wall interaction, w , in this work, we have classified w into three regions ( w>0.9 , 0.1< or =w< or =0.9 , and w<0.1 ), which are denoted as strongly, moderately, and weakly attractive fluid-wall interaction, respectively. The dependence of hysteresis on the fluid-wall interaction is interpreted by the different nucleation mechanisms. Our constrained LDFT calculations also show that the different transition paths may induce different nucleation behaviors. The transition path dependence should be considered if morphological transition of nuclei exists during a nucleation process.

Molecular-dynamics simulation of evaporation processes of fluid bridges confined in slitlike pores

A simple fluid, described by pointlike particles interacting via the Lennard-Jones potential, is considered under confinement in a slit geometry between two walls at distance L_{z} apart for densities inside the vapor-liquid coexistence curve. Equilibrium then requires the coexistence of a liquid "bridge" between the two walls, and vapor in the remaining pore volume. We study this equilibrium for several choices of the wall-fluid interaction (corresponding to the full range from complete wetting to complete drying, for a macroscopically thick film), and consider also the kinetics of state changes in such a system. In particular, we study how this equilibrium is established by diffusion processes, when a liquid is inserted into an initially empty capillary (partial or complete evaporation into vacuum), or when the volume available for the vapor phase increases. We compare the diffusion constants describing the rates of these processes in such inhomogeneous systems to the diffusion constants in the corresponding bulk liquid and vapor phases.

Nanodrop on a nanorough solid surface: density functional theory considerations

The density distributions and contact angles of liquid nanodrops on nanorough solid surfaces are determined on the basis of a nonlocal density functional theory. Two kinds of roughness, chemical and physical, are examined. The former considers the substrate as a sequence of two kinds of semi-infinite vertical plates of equal thicknesses but of different natures with different strengths for the liquid-solid interactions. The physical roughness involves an ordered set of pillars on a flat homogeneous surface. Both hydrophobic and hydrophilic surfaces were considered. For the chemical roughness, the contact angle which the drop makes with the flat surface increases when the strength of the liquid-solid interaction for one kind of plates decreases with respect to the fixed value of the other kind of plates. Such a behavior is in agreement with the Cassie-Baxter expression derived from macroscopic considerations. For the physical roughness on a hydrophobic surface, the contact angle which a drop makes with the plane containing the tops of the pillars increases with increasing roughness. Such a behavior is consistent with the Wenzel formula developed for macroscopic drops. For hydrophilic surfaces, as the roughness increases the contact angle first increases, in contradiction with the Wenzel formula, which predicts for hydrophilic surfaces a decrease of the contact angle with increasing roughness. However, a further increase in roughness changes nonmonotonously the contact angle, and at some roughness, the drop disappears and only a liquid film is present on the surface. It was also found that the contact angle has a periodic dependence on the volume of the drop.

Nucleation of fluids confined between parallel walls: a lattice Monte Carlo study

Nucleation phenomena in lattice gas models of simple and chain molecules confined in slitlike pores are studied using Monte Carlo methods. Finite-size scaling is used to investigate the nature of phase transitions accompanying the formation of layers at the pore walls. It is demonstrated that nucleation leads to the symmetry breaking and the formation of nuclei at one wall only.

Symmetry breaking in binary mixtures in closed nanoslits

The symmetry breaking (SB) of the fluid density distribution (FDD) in closed nanoslits between two identical parallel solid walls described by Berim and Ruckenstein [J. Chem. Phys. 128, 024704 (2008)] for a single component fluid is examined for binary mixtures on the basis of a nonlocal canonical ensemble density functional theory. As in Monte Carlo simulations, the periodicity of the FDD in one of the lateral (parallel to the wall surfaces) directions, denoted as the x direction, was assumed. In the other lateral direction, y direction, the FDD was considered to be uniform. The molecules of the two components have different diameters and their Lennard-Jones interaction potentials have different energy parameters. It was found that depending on the average fluid density in the slit and mixture composition, SB can occur for both or none of the components but never for only one of them. In the direction perpendicular to the walls (h direction), the FDDs of both components can be asymmetrical about the middle plane between walls. In the x direction, the SB occurs as bumps and bridges enriched in one of the components, whereas the composition of the mixture between them is enriched in the other component. The dependence of the SB states on the length Lx of the FDD period at fixed average densities of the two components was examined for Lx in the range from 10 to 120 molecular diameters of the smaller size component. It was shown that for large Lx, the stable state of the system corresponds to a bridge. Because the free energy of that state decreases monotonically with increasing Lx, one can conclude that the real period is very large (infinite) and that a single bridge exists in the slit.

Two-dimensional symmetry breaking of fluid density distribution in closed nanoslits

Stable and metastable fluid density distributions (FDDs) in a closed nanoslit between two identical parallel solid walls have been identified on the basis of a nonlocal canonical ensemble density functional theory. Similar to Monte Carlo simulations, periodicity of the FDD in one of the lateral (parallel to the walls surfaces) directions, denoted as the x direction, was assumed. In the other lateral direction, y direction, the FDD was considered uniform. It was found that depending on the average fluid density in the slit, both uniform as well as nonuniform FDDs in the x direction can occur. The uniform FDDs are either symmetric or asymmetric about the middle plane between walls; the latter FDD being the consequence of a symmetry breaking across the slit. The nonuniform FDDs in the x direction occur either in the form of a bump on a thin liquid film covering the walls or as a liquid bridge between those walls and provide symmetry breaking in the x direction. For small and large average densities, the stable state is uniform in the x direction and is symmetric about the middle plane between walls. In the intermediate range of the average density and depending on the length L(x) of the FDD period, the stable state can be represented either by a FDD, which is uniform in the x direction and asymmetric about the middle of the slit (small values of L(x)), or by a bump- and bridgelike FDD for intermediate and large values of L(x), respectively. These results are in agreement with the Monte Carlo simulations performed earlier by other authors. Because the free energy of the stable state decreases monotonically with increasing L(x), one can conclude that the real period is very large (infinite) and that for the values of the parameters employed, a single bridge of finite length over the entire slit is generated.

Cell dynamics simulation of droplet and bridge formation within striped nanocapillaries

The kinetics of droplet and bridge formation within striped nanocapillaries is studied when the wetting film grows via interface-limited growth. The phenomenological time-dependent Ginzburg-Landau (TDGL)-type model with thermal noise is used and numerically solved using the cell dynamics method. The model is two-dimensional and consists of undersaturated vapor confined within a nanocapillary made of two infinitely wide flat substrates. The surface of the substrate is chemically heterogeneous with a single stripe of lyophilic domain that exerts long-range attractive potential to the vapor molecule. The dynamics of nucleation and subsequent growth of droplet and bridge can be simulated and visualized. In particular, the evolution of the morphology from droplet or bump to bridge is clearly identified. The crucial role played by the substrate potential on the morphology of bridge of nanoscopic size is clarified. Nearly temperature-independent evolution of capillary condensation is predicted when the interface-limited growth dominates. In addition, it is shown that the dynamics of capillary condensation follows the scenario of capillary condensation proposed by Everett and Haynes three decades ago.

Water as a lubricant for graphite: a computer simulation study

The phase state and shear behavior of water confined between parallel graphite sheets are studied using the grand canonical Monte Carlo technique and TIP4P model for water. In describing the water-graphite interaction, two orientation-dependent potentials are tried. Both potentials are fitted to many-body polarizable model predictions for the binding energy and the equilibrium conformation of the water-graphite complex [K. Karapetian and K. D. Jordan in Water in Confining Geometries, edited by V. Buch and J. P. Devlin (Springer, Berlin, 2003), pp. 139-150]. Based on the simulation results, the property of water to serve as a lubricant between the rubbing surfaces of graphitic particles is associated, first, with the capillary condensation of water occurring in graphitic pores of monolayer width and, second, with the fact that the water monolayer compressed between graphite particles retains a liquidlike structure and offers only slight resistance to shear.

Filling and emptying transitions in cylindrical channels: a density functional approach

The authors use density functional theory in a square gradient approximation to investigate capillary condensation and evaporation in cylindrical channels of finite lengths. The model allows them to systematically explore the effect of the pore's length, width, and surface fields on the location of the transition between "empty" (vapor-filled) and "full" (liquid-filled) states. In general, their results indicate that decreasing the length of the channel drastically reduces the range of pore widths where a transition between liquidlike and vaporlike configurations may be observed. For the wide pores, the transition occurs at very low pressures where the liquid is no longer stable, while for the narrow pores, the transition is hindered by the solid-fluid interactions that favor the vapor phase in lyophobic pores. For the limited range of sizes where the transition can occur, the authors' results confirm the existence of two competing minima that may explain the density oscillations observed in a computer simulation of nanochannels. Comparisons between these results with those generated using a phenomenological model based on the capillary approximation indicate that this simplified approach yields fairly good predictions for medium size pores. However, the capillary approach fails to properly describe the properties of the very small and very large pores.

Heterogeneous nucleation in and out of pores

We study the nucleation of a new thermodynamic phase in pores and find that the nucleation often proceeds via two steps: nucleation of pore filling, and nucleation out of the pore. These two rates have opposing dependencies on pore size, resulting in a pore size at which the nucleation rate of the new phase is maximal. This finding is relevant to attempts to design and use porous media to crystallize proteins.

Modeling of Adsorption and Nucleation in Infinite Cylindrical Pores by Two-Dimensional Density Functional Theory

In this paper, we present an analysis of argon adsorption in cylindrical pores having amorphous silica structure by means of a nonlocal density functional theory (NLDFT). In the modeling, we account for the radial and longitudinal density distributions, which allow us to consider the interface between the liquidlike and vaporlike fluids separated by a hemispherical meniscus in the canonical ensemble. The Helmholtz free energy of the meniscus was determined as a function of pore diameter. The canonical NLDFT simulations show the details of density rearrangement at the vaporlike and liquidlike spinodal points. The limits of stability of the smallest bridge and the smallest bubble were also determined with the canonical NLDFT. The energy of nucleation as a function of the bulk pressure and the pore diameter was determined with the grand canonical NLDFT using an additional external potential field. It was shown that the experimentally observed reversibility of argon adsorption isotherms at its boiling point up to the pore diameter of 4 nm is possible if the potential barrier of 22kT is overcome due to density fluctuations.

Nucleation on cylindrical plates: sharp transitions and double barriers

We apply methods of density-functional theory in statistical mechanics to study the properties of droplets and bubbles formed on a single cylindrical plate or between two such disks immersed in a metastable fluid. Our approach allows us to analyze the properties of different types of aggregates and investigate the effect of disk size, disk separation, and solid-fluid interactions on the dynamics of a liquid-vapor phase transition. The finite size of disks induces nucleation phenomena that are not observed in the cases of either a planar wall or a slit pore. Heterogeneous nucleation on a single disk is characterized by the existence of two distinct types of critical nuclei that control the phase-transition dynamics at different supersaturations. Asymmetric droplets or bubbles formed on one side of the disk are the preferred nucleation path at high supersaturations. However, these types of aggregates become unstable close to the binodal, where they abruptly collapse into nuclei that engulf the cylindrical plates. Droplet or bubble nucleation in between two disks may occur through a free-energy barrier with one or two maxima depending on the value of the system parameters and the supersaturation. Metastable droplets or bubbles corresponding to local minima of the free energy are observed forming between two plates only after density fluctuations in the system achieve a critical size. These types of aggregates only exist for cylindrical plates larger than a minimum size given a fixed distance between the disks. The stability of these droplets and bubbles decreases when the plates are separated.

Nucleation in Hydrophobic Cylindrical Pores: A Lattice Model

We consider the nucleation process associated with capillary condensation of a vapor in a hydrophobic cylindrical pore (capillary evaporation). The liquid-vapor transition is described within the framework of a simple lattice model. The phase properties are characterized both at the mean-field level and with Monte Carlo simulations. The nucleation process for the liquid to vapor transition is then specifically considered. Using umbrella sampling techniques, we show that nucleation occurs through the condensation of an asymmetric vapor bubble at the pore surface. Even for highly confined systems, good agreement is found with macroscopic considerations based on classical nucleation theory. The results are discussed in the context of recent experimental work on the extrusion of water in hydrophobic pores.

Intrusion and extrusion of water in hydrophobic mesopores

We present experimental and theoretical results on intrusion-extrusion cycles of water in hydrophobic mesoporous materials, characterized by independent cylindrical pores. The intrusion, which takes place above the bulk saturation pressure, can be well described using a macroscopic capillary model. Once the material is saturated with water, extrusion takes place upon reduction of the externally applied pressure. Our results for the extrusion pressure can only be understood by assuming that the limiting extrusion mechanism is the nucleation of a vapor bubble inside the pores. A comparison of calculated and experimental nucleation pressures shows that a proper inclusion of line tension effects is necessary to account for the observed values of nucleation barriers. Negative line tensions of order 10(-11) J m(-1) are found for our system, in reasonable agreement with other experimental estimates of this quantity.

The structure of fluids confined in crystalline slitlike nanoscopic pores: Bilayers

Grand canonical and canonical ensemble Monte Carlo simulation methods are used to study the structure and phase behavior of Lennard-Jones fluids confined between the parallel (100) planes of the face centered cubic crystal. Ultra thin slit pores of the width allowing for the formation of only two adsorbate layers are considered. It is demonstrated that the structure of adsorbed phases is very sensitive to the wall-wall separation and to the strength of the fluid-wall potential. It is also shown that the structure of low temperature (solid) phases strongly depends on the fluid density. In particular, when the surface field is sufficiently strong, then the high density phases may exhibit a domain wall structure, quite the same as found in monolayer films adsorbed at a single substrate wall. On the other hand, the weakening of the surface potential leads to the regime in which only the hexagonally ordered bilayer structure is stable. The phase diagrams for a series of systems are estimated. It is shown that, depending on the pore width and the temperature, the condensation leads to the formation of the commensurate or incommensurate phases. The incommensurate phases may have the domain-wall or the hexagonal structure depending on the pore width and the strength of the fluid-wall potential.

Nucleation in cylindrical capillaries

We use a local density functional theory in the square gradient approximation to explore the properties of critical nuclei for the liquid-vapor transition of van der Waals fluids in cylindrical capillaries. The proposed model allows us to investigate the effect of pore size, surface field, and supersaturation on the behavior of the system. Our calculations predict the existence of at least three different pathways for the nucleation of droplets and bubbles in these confined fluids: axisymmetric annular bumps and lenses, and asymmetric droplets. The morphological transition between these different structures is driven by the existence of states of zero compressibility in the capillary. We show that the classical capillarity theory provides surprisingly accurate predictions for the work of formation of critical nuclei in cylindrical pores when line tension contributions to the free energy are taken into account.